Mass on a spring oscillation problem

[Katy96]

Homework Statement

Homework Equations

The Attempt at a Solution

any help would be appreciated! I keep trying and just keep getting stuck really early on.

 

[SteamKing]

"getting stuck really early on" does not provide sufficient information to help you.

Please show what work you've done on this problem, or tell us what you don't understand about the question.

 

[Katy96]

I don't understand where the first differential comes from

 

[SteamKing]

I don't understand where the first differential comes from

I suppose you mean Equation 1?

Do you know what ΣF = ma means?

 

[Katy96]

yes force= mass*acceleration

 

[SteamKing]

yes force= mass*acceleration

And how would you apply ΣF = ma to the problem with the mass and spring?

 

[Katy96]

that's where I get stuck

 

[SteamKing]

that's where I get stuck

Well, what forces are acting on the mass? If you assume the mass is at rest at point O, and you move it x-distance to the right, what happens to the spring? What does the displacement of the spring do to the mass?

 

[Katy96]

Well, what forces are acting on the mass? If you assume the mass is at rest at point O, and you move it x-distance to the right, what happens to the spring? What does the displacement of the spring do to the mass?

the spring is stretched so will want to go back to its original place

 

[SteamKing]

the spring is stretched so will want to go back to its original place

Yes, but what does the tendency of the spring to unstretch itself do to the mass? What does it take to stretch the spring in the first place?

 

[Katy96]

Yes, but what does the tendency of the spring to unstretch itself do to the mass? What does it take to stretch the spring in the first place?

it has to be stretched by something and to go back to its original it passes and oscillates

 

[SteamKing]

it has to be stretched by something and to go back to its original it passes and oscillates

What is this something? Do you know about Hooke's Law?

https://en.wikipedia.org/wiki/Hooke's_law

 

[Katy96]

What is this something? Do you know about Hooke's Law?

https://en.wikipedia.org/wiki/Hooke's_law

yeah F=-kX

 

[SteamKing]

yeah F=-kX

In your problem, you move the mass a distance x. What does that create in the spring? Make the mass a free body and label all the forces acting on it.

 

[TomW17]

that's where I get stuck

First thing's first: you need to draw a good free body diagram. Label all the forces acting on the mass and their directions. The sum of these forces will be equal to the mass * the acceleration of the body (remember $a(t) = \ddot{x}(t)$) , and the required DE will fall out pretty quickly from this.